Finite Group Databasebeta

← D47×#2395 #26382516

Subgroups — D47×#2395 #26382516

Order 12032.

3182 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×#117×D47C211yesmaximal, characteristic, complemented
3#20246654C211yesmaximal, characteristic, complemented
4#20246653C211yesmaximal, characteristic, complemented
5#20246652C211yesmaximal, characteristic, complemented
6#20246651C212yesmaximal, complemented
7#20246650C211yesmaximal, characteristic, complemented
8#20246649C212yesmaximal, complemented
9#20246648C211yesmaximal, characteristic, complemented
10#20246647C211yesmaximal, characteristic, complemented
11#20246646C212yesmaximal, complemented
12#20246645C211yesmaximal, characteristic, complemented
13#20246644C212yesmaximal, complemented
14#400×D47C211yesmaximal, characteristic, complemented
15#399×D47C211yesmaximal, characteristic, complemented
16#398×D47C211yesmaximal, characteristic, complemented
17#397×D47C211yesmaximal, characteristic, complemented
18#397×D47C212yesmaximal, complemented
19#394×D47C212yesmaximal
20C4×C4⋊C4×D47C212yesmaximal, complemented
21C4×C22⋊C4×D47C212yesmaximal, complemented
22C4×C22⋊C4×D47C211yesmaximal, characteristic, complemented
23C47×#2395C211yesmaximal, characteristic, complemented
24C22×D4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×D4×Dic47C2211yescharacteristic
29C2×#13093986C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×(C22⋊D47)⋊C4C2211yescharacteristic
33C2×(C22⋊D47)⋊C4C2211yescharacteristic
34C4×D4×D47—28no—
35C2×#13093983C2211yescharacteristic, complemented
36C2×#13093982C2211yescharacteristic, complemented
37C2×#13093982C2211yescharacteristic, complemented
38C2×#13093981C2212yescomplemented
39C2×#13093980C2212yescomplemented
40#117×D47—28no—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C4⋊C4×D47C2212yes—
45C2×C4⋊C4×D47C2212yes—
46C2×C22⋊C4×D47C2212yes—
47C2×C22⋊C4×D47C2211yescharacteristic
48C2×C22⋊C4×D47C2211yescharacteristic
49C2×C22⋊C4×D47C2212yes—
50C2×C22⋊C4×D47C2212yes—
51C2×C22⋊C4×D47C2212yes—
52C2×C42×D47C2212yes—
53C2×C42×D47C2211yescharacteristic
54C2×C42×D47C2212yes—
55#15689065C2212yescomplemented
56#15689064C2212yescomplemented
57#15689063C2211yescharacteristic, complemented
58#15689062C2211yescharacteristic, complemented
59#15689061C2211yescharacteristic, complemented
60#15689060C2211yescharacteristic, complemented
61#15689059C2212yescomplemented
62#15689059C2211yescharacteristic, complemented
63#15689058C2211yescharacteristic, complemented
64#15689058C2212yescomplemented
65#15689057C2212yescomplemented
66#15689056C2212yescomplemented
67#15689055C2211yescharacteristic, complemented
68#15689054C2211yescharacteristic, complemented
69#15689053C2211yescharacteristic, complemented
70#15689052C2212yescomplemented
71#15689052C2212yescomplemented
72#15689052C2212yescomplemented
73#15689051C2212yescomplemented
74#15689051C2212yescomplemented
75#15689051C2212yescomplemented
76#15689050C2211yescharacteristic, complemented
77#15689050C2212yescomplemented
78#15689049C2211yescharacteristic, complemented
79#15689049C2212yescomplemented
80#15689048C2212yescomplemented
81#15689048C2211yescharacteristic, complemented
82#15689041C2212yes—
83#15689040C2212yes—
84#15689039C2212yes—
85#15689039C2212yes—
86#15689038C2212yes—
87#15689038C2212yes—
88#15689037C2212yes—
89C4⋊C4×Dic47C2212yescomplemented
90C4⋊C4×Dic47C2212yescomplemented
91C4×Dic47⋊C4C2212yescomplemented
92C4×Dic47⋊C4C2212yescomplemented
93C4×C4⋊Dic47C2212yescomplemented
94#15688974C2212yescomplemented
95#15688974C2212yescomplemented
96C22⋊C4×Dic47C2212yescomplemented
97C22⋊C4×Dic47C2212yescomplemented
98C22⋊C4×Dic47C2212yescomplemented
99C4×(C2×D47)⋊C4C2212yescomplemented
100C4×(C2×D47)⋊C4C2212yescomplemented
101C4×(C2×D47)⋊C4C2212yescomplemented
102C4×C22⋊Dic47C2211yescharacteristic, complemented
103C4×C22⋊Dic47C2212yescomplemented
104#15688970C2212yescomplemented
105#15688970C2212yescomplemented
106#15688970C2211yescharacteristic, complemented
107#15688970C2211yescharacteristic, complemented
108#95×D47C2212yes—
109#95×D47C2212yes—
110#95×D47C2212yes—
111#95×D47C2211yescharacteristic
112#95×D47C2212yes—
113#95×D47C2211yescharacteristic
114C2×C4×D4×C47C2211yescharacteristic
115C2×#117×C47C2211yescharacteristic, complemented
116C47×#400C2211yescharacteristic, complemented
117C47×#399C2211yescharacteristic, complemented
118C47×#398C2211yescharacteristic, complemented
119C47×#397C2212yescomplemented
120C47×#397C2211yescharacteristic, complemented
121C47×#394C2212yes—
122C4×C4⋊C4×C47C2212yescomplemented
123C4×C22⋊C4×C47C2211yescharacteristic, complemented
124C4×C22⋊C4×C47C2212yescomplemented
125C24×D47C2311yescharacteristic
126C24×D47C2311yescharacteristic
127C22×D188C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C22×C22⋊D47C2311yescharacteristic
130C2×D4×D47—24no—
131C2×D4×D47—24no—
132C2×D4×D47—24no—
133C23×Dic47C2311yescharacteristic
134C23×Dic47C2311yescharacteristic
135C22×C4×D47—28no—
136C22×C4×D47—24no—
137C22×C4×D47—28no—
138C22×C4×D47D418yes—
139C22×C4×D47C2312yes—
140C22×C4×D47C2311yescharacteristic
141C22×C4×D47C2311yescharacteristic
142C22×C4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2312yes—
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C4×D188—24no—
153D4×Dic47—24no—
154#13093986—24no—
155C4×C22⋊D47—24no—
156C4×C22⋊D47—24no—
157(C22⋊D47)⋊C4—24no—
158(C22⋊D47)⋊C4—24no—
159#13093983—24no—
160#13093982—24no—
161#13093982—24no—
162#13093981—28no—
163#13093980—28no—
164C2×C4⋊Dic47C2312yes—
165C2×C4⋊Dic47C2312yes—
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2311yescharacteristic
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C2×Dic47⋊C4C2312yes—
173C2×Dic47⋊C4C2312yes—
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C2×Dic47⋊C4C2312yes—
177C4⋊C4×D47—24no—
178C4⋊C4×D47—24no—
179C4⋊C4×D47—24no—
180C4⋊C4×D47—28no—
181C4⋊C4×D47—28no—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2312yes—
184C2×C22⋊Dic47C2312yes—
185C2×C22⋊Dic47C2312yes—
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2311yescharacteristic
188C2×(C2×D47)⋊C4C2312yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C2×(C2×D47)⋊C4C2311yescharacteristic
200C22⋊C4×D47—28no—
201C22⋊C4×D47—24no—
202C22⋊C4×D47—28no—
203C22⋊C4×D47—24no—
204C22⋊C4×D47—28no—
205C22⋊C4×D47—28no—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2312yes—
209C2×C4×Dic47C2312yes—
210C2×C4×Dic47C2312yes—
211C2×C4×Dic47C2312yes—
212C2×C4×Dic47C2311yescharacteristic
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C42×D47—28no—
216C42×D47—24no—
217C42×D47—28no—
218C47⋊#95C2311yescharacteristic
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2311yescharacteristic
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C22×D4×C47C2311yescharacteristic
235C23×C4×C47C2311yescharacteristic
236C23×C4×C47C2311yescharacteristic
237C4×D4×C47—24no—
238#117×C47—24no—
239C2×C4⋊C4×C47C2312yes—
240C2×C4⋊C4×C47C2312yes—
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C22⋊C4×C47C2312yes—
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2311yescharacteristic
249C2×C22⋊C4×C47C2311yescharacteristic
250C2×C42×C47C2312yes—
251C2×C42×C47C2312yes—
252C2×C42×C47C2311yescharacteristic
253#95×C47C2312yes—
254#95×C47C2311yescharacteristic
255#95×C47C2312yes—
256#95×C47C2311yescharacteristic
257#95×C47C2312yes—
258#95×C47C2312yes—
259C24×C47C2411yescharacteristic
260C24×C47C2411yescharacteristic
261C23×D47—22no—
262C23×D47—24no—
263C23×D47—24no—
264C23×D47—24no—
265C23×D47—24no—
266C23×D47—22no—
267C23×D47—22no—
268C23×D47—22no—
269C23×D47C2×D414yes—
270C23×D47#4114yes—
271C23×D47C2411yescharacteristic
272C23×D47C2411yescharacteristic
273C23×D47C2411yescharacteristic
274C2×D4×C47—22no—
275C2×D4×C47—22no—
276C2×D4×C47—22no—
277C22×C4×C47—24no—
278C22×C4×C47—22no—
279C22×C4×C47—24no—
280C22×C4×C47C2×D414yes—
281C22×C4×C47C2412yes—
282C22×C4×C47C2412yes—
283C22×C4×C47C2411yescharacteristic
284C22×C4×C47C2412yes—
285C22×C4×C47C2411yescharacteristic
286C22×C4×C47C2411yescharacteristic
287C22×C4×C47C2412yes—
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C2×C22⋊D47—22no—
291C2×C22⋊D47—22no—
292C2×C22⋊D47—22no—
293C2×C22⋊D47—22no—
294C2×C22⋊D47—22no—
295C2×C22⋊D47—22no—
296C22×Dic47—24no—
297C22×Dic47—22no—
298C22×Dic47—24no—
299C22×Dic47C2×D414yes—
300C22×Dic47C2412yes—
301C22×Dic47C2411yescharacteristic
302C22×Dic47C2412yes—
303C22×Dic47C2412yes—
304C22×Dic47C2411yescharacteristic
305C22×Dic47C2411yescharacteristic
306C22×Dic47C2412yes—
307C22×Dic47C2411yescharacteristic
308C22×Dic47C2411yescharacteristic
309D4×D47—232no—
310C2×D188—22no—
311C2×D188—22no—
312C2×D188—22no—
313C2×C4×D47—22no—
314C2×C4×D47—24no—
315C2×C4×D47—24no—
316C2×C4×D47—24no—
317C2×C4×D47—22no—
318C2×C4×D47—24no—
319C2×C4×D47—24no—
320C2×C4×D47—232no—
321C2×C4×D47—22no—
322C2×C4×D47—24no—
323C2×C4×D47—24no—
324C2×C4×D47—22no—
325C2×C4×D47—24no—
326C2×C4×D47—24no—
327C2×C4×D47—24no—
328C2×C4×D47—24no—
329C2×C4×D47—24no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—24no—
333C2×C4×D47—24no—
334C2×C4×D47—22no—
335C2×C4×D47—24no—
336C2×C4×D47—22no—
337C2×C4×D47—24no—
338C2×C4×D47—416no—
339C2×C4×D47C2×D414yes—
340C2×C4×D47C2×D414yes—
341C2×C4×D47C2×D414yes—
342C2×C4×D47C2×D414yes—
343C2×C4×D47#4118yes—
344C2×C4×D47#4114yes—
345C2×C4×D47#4118yes—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—22no—
348C4⋊C4×C47—22no—
349C4⋊C4×C47—24no—
350C4⋊C4×C47—24no—
351C22⋊C4×C47—24no—
352C22⋊C4×C47—22no—
353C22⋊C4×C47—24no—
354C22⋊C4×C47—22no—
355C22⋊C4×C47—24no—
356C22⋊C4×C47—24no—
357C42×C47—24no—
358C42×C47—22no—
359C42×C47—24no—
360C22⋊Dic47—24no—
361C22⋊Dic47—22no—
362C22⋊Dic47—24no—
363C22⋊Dic47—22no—
364C22⋊Dic47—24no—
365C22⋊Dic47—24no—
366(C2×D47)⋊C4—24no—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—22no—
369(C2×D47)⋊C4—22no—
370(C2×D47)⋊C4—24no—
371(C2×D47)⋊C4—24no—
372(C2×D47)⋊C4—22no—
373(C2×D47)⋊C4—24no—
374(C2×D47)⋊C4—24no—
375(C2×D47)⋊C4—22no—
376(C2×D47)⋊C4—24no—
377(C2×D47)⋊C4—24no—
378C4⋊Dic47—22no—
379C4⋊Dic47—22no—
380C4⋊Dic47—24no—
381C4⋊Dic47—22no—
382C4⋊Dic47—24no—
383Dic47⋊C4—22no—
384Dic47⋊C4—24no—
385Dic47⋊C4—24no—
386Dic47⋊C4—24no—
387Dic47⋊C4—22no—
388Dic47⋊C4—24no—
389Dic47⋊C4—24no—
390Dic47⋊C4—24no—
391C4×Dic47—24no—
392C4×Dic47—22no—
393C4×Dic47—24no—
394C4×Dic47—24no—
395C4×Dic47—24no—
396C4×Dic47—22no—
397C4×Dic47—22no—
398C4×Dic47—24no—
399C4×Dic47—24no—
400C23×C47—21no—
401C23×C47—22no—
402C23×C47—22no—
403C23×C47—22no—
404C23×C47—22no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47C22×D412yes—
409C23×C47C2×#4112yes—
410C23×C47C2511yescharacteristic
411C22×D47—21no—
412C22×D47—22no—
413C22×D47—22no—
414C22×D47—22no—
415C22×D47—22no—
416C22×D47—21no—
417C22×D47—21no—
418C22×D47—21no—
419C22×D47—28no—
420C22×D47—28no—
421C22×D47—28no—
422C22×D47—216no—
423C22×D47—28no—
424C22×D47—44no—
425C22×D47—48no—
426C22×D47—48no—
427C22×D47—48no—
428C22×D47—44no—
429C22×D47C22×D412yes—
430C22×D47C22×D412yes—
431C22×D47C2×#4112yes—
432C22×D47C2×#4114yes—
433C22×D47C2×#4112yes—
434C22×D47C2×#4112yes—
435C22×D47C2×#4114yes—
436D4×C47—28no—
437C2×C4×C47—21no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—21no—
442C2×C4×C47—28no—
443C2×C4×C47—22no—
444C2×C4×C47—22no—
445C2×C4×C47—21no—
446C2×C4×C47—21no—
447C2×C4×C47—22no—
448C2×C4×C47—22no—
449C2×C4×C47—22no—
450C2×C4×C47—22no—
451C2×C4×C47—22no—
452C2×C4×C47—22no—
453C2×C4×C47—22no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—44no—
457C2×C4×C47C22×D412yes—
458C2×C4×C47C22×D412yes—
459C2×C4×C47C2×#4112yes—
460C2×C4×C47C2×#4114yes—
461C2×C4×C47C2×#4114yes—
462C22⋊D47—28no—
463C22⋊D47—28no—
464C2×Dic47—21no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—21no—
469C2×Dic47—28no—
470C2×Dic47—22no—
471C2×Dic47—22no—
472C2×Dic47—21no—
473C2×Dic47—21no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—22no—
477C2×Dic47—22no—
478C2×Dic47—22no—
479C2×Dic47—22no—
480C2×Dic47—22no—
481C2×Dic47—22no—
482C2×Dic47—22no—
483C2×Dic47—44no—
484C2×Dic47C22×D412yes—
485C2×Dic47C22×D412yes—
486C2×Dic47C2×#4112yes—
487C2×Dic47C2×#4114yes—
488C2×Dic47C2×#4114yes—
489D188—28no—
490C4×D47—28no—
491C4×D47—28no—
492C4×D47—216no—
493C4×D47—28no—
494C4×D47—28no—
495C4×D47—44no—
496C4×D47—48no—
497C4×D47—48no—
498C4×D47—44no—
499C4×D47—48no—
500C4×D47—44no—
501C4×D47—44no—
502C4×D47#123116yes—
503C2×#2395—471nomaximal, Sylow
504C22×C47—22no—
505C22×C47—22no—
506C22×C47—22no—
507C22×C47—24no—
508C22×C47—22no—
509C22×C47—41no—
510C22×C47—42no—
511C22×C47—42no—
512C22×C47—42no—
513C22×C47—41no—
514C22×C47C23×D411yescharacteristic
515C22×C47C22×#4112yes—
516C22×C47C22×#4111yescharacteristic
517C22×C47C22×#4111yescharacteristic
518C22×C47C22×#4112yes—
519C2×D47—22no—
520C2×D47—22no—
521C2×D47—22no—
522C2×D47—24no—
523C2×D47—22no—
524C2×D47—41no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47—42no—
528C2×D47—41no—
529C2×D47—416no—
530C2×D47—416no—
531C2×D47C2×#12314yes—
532C2×D47#52514yes—
533C2×D47#52918yes—
534C2×D47#52918yes—
535C2×D47#53214yes—
536C4×C47—22no—
537C4×C47—22no—
538C4×C47—24no—
539C4×C47—41no—
540C4×C47—42no—
541C4×C47—42no—
542C4×C47—42no—
543C4×C47—41no—
544C4×C47C2×#12314yes—
545Dic47—22no—
546Dic47—22no—
547Dic47—24no—
548Dic47—41no—
549Dic47—42no—
550Dic47—42no—
551Dic47—42no—
552Dic47—41no—
553Dic47C2×#12314yes—
554C22×C4×D4—471no—
555C22×#117—471no—
556#2395—471no—
557#2395—471no—
558#2395—471no—
559#2395—472no—
560#2395—471no—
561#2395—472no—
562#2395—472no—
563#2395—471no—
564#2395—472no—
565#2395—471no—
566#2395—471no—
567#2395D4711yescharacteristic, direct product factor
568C2×#400—471no—
569C2×#399—471no—
570C2×#398—471no—
571C2×#397—472no—
572C2×#397—471no—
573C2×#394—472no—
574C2×C4×C4⋊C4—472no—
575C2×C4×C22⋊C4—471no—
576C2×C4×C22⋊C4—472no—
577C2×C47—42no—
578C2×C47—42no—
579C2×C47C22×#12311yescharacteristic
580C2×C47C2×#52511yescharacteristic
581C2×C47C2×#52912yes—
582C2×C47C2×#52912yes—
583C2×C47C2×#53211yescharacteristic
584D47—42no—
585D47—42no—
586D47#239518yesdirect product factor
587C23×D4—471no—
588C24×C4—471no—
589C24×C4—471no—
590C2×C4×D4—471no—
591C2×C4×D4—471no—
592C2×C4×D4—471no—
593C2×C4×D4—471no—
594C2×C4×D4—471no—
595C2×C4×D4—471no—
596C2×C4×D4—471no—
597C2×C4×D4—948no—
598C2×C4×D4C2×D4711yescharacteristic
599C2×#117—471no—
600C2×#117—471no—
601C2×#117—471no—
602C2×#117—472no—
603C2×#117—472no—
604C2×#117—948no—
605C2×#117C2×D4711yescharacteristic, complemented
606C22×C4⋊C4—472no—
607C22×C4⋊C4—471no—
608C22×C4⋊C4—472no—
609C22×C4⋊C4—471no—
610C22×C4⋊C4—471no—
611C22×C22⋊C4—472no—
612C22×C22⋊C4—472no—
613C22×C22⋊C4—472no—
614C22×C22⋊C4—472no—
615C22×C22⋊C4—471no—
616C22×C22⋊C4—471no—
617C22×C42—472no—
618C22×C42—471no—
619C22×C42—472no—
620#400—471no—
621#400—471no—
622#400—471no—
623#400—472no—
624#400—472no—
625#400C2×D4711yescharacteristic, complemented
626#399—472no—
627#399—471no—
628#399—472no—
629#399—471no—
630#399—471no—
631#399C2×D4711yescharacteristic, complemented
632#398—471no—
633#398—471no—
634#398—472no—
635#398—471no—
636#398—472no—
637#398C2×D4711yescharacteristic, complemented
638#397—472no—
639#397—471no—
640#397—472no—
641#397—471no—
642#397—472no—
643#397—472no—
644#397—472no—
645#397—472no—
646#397—471no—
647#397—472no—
648#397—472no—
649#397—472no—
650#397C2×D4712yescomplemented
651#397C2×D4711yescharacteristic, complemented
652#394—472no—
653#394—472no—
654#394—472no—
655#394—472no—
656#394—472no—
657#394—472no—
658#394—472no—
659#394C2×D4712yes—
660C4×C4⋊C4—472no—
661C4×C4⋊C4—472no—
662C4×C4⋊C4—472no—
663C4×C4⋊C4—472no—
664C4×C4⋊C4—472no—
665C4×C4⋊C4—472no—
666C4×C4⋊C4—472no—
667C4×C4⋊C4C2×D4712yescomplemented
668C4×C22⋊C4—472no—
669C4×C22⋊C4—471no—
670C4×C22⋊C4—472no—
671C4×C22⋊C4—472no—
672C4×C22⋊C4—472no—
673C4×C22⋊C4—472no—
674C4×C22⋊C4—472no—
675C4×C22⋊C4—472no—
676C4×C22⋊C4—472no—
677C4×C22⋊C4—472no—
678C4×C22⋊C4—471no—
679C4×C22⋊C4—471no—
680C4×C22⋊C4C2×D4712yescomplemented
681C4×C22⋊C4C2×D4711yescharacteristic, complemented
682C2×#95—472no—
683C2×#95—472no—
684C2×#95—472no—
685C2×#95—471no—
686C2×#95—472no—
687C2×#95—471no—
688C47C2×#239511yescharacteristic, complemented, Sylow
689C25—471no—
690C25—471no—
691C22×D4—471no—
692C22×D4—471no—
693C22×D4—471no—
694C22×D4—944no—
695C22×D4—944no—
696C22×D4—944no—
697C22×D4C22×D4711yescharacteristic
698C23×C4—471no—
699C23×C4—471no—
700C23×C4—478no—
701C23×C4—472no—
702C23×C4—471no—
703C23×C4—471no—
704C23×C4—471no—
705C23×C4—471no—
706C23×C4—471no—
707C23×C4—471no—
708C23×C4—472no—
709C23×C4—472no—
710C23×C4—472no—
711C23×C4—471no—
712C23×C4—471no—
713C23×C4—471no—
714C23×C4—948no—
715C23×C4—944no—
716C23×C4—948no—
717C23×C4C22×D4711yescharacteristic
718C23×C4C22×D4711yescharacteristic
719C4×D4—24no—
720C4×D4—944no—
721C4×D4—944no—
722C4×D4—944no—
723C4×D4—944no—
724C4×D4—944no—
725C4×D4—944no—
726C4×D4—944no—
727#117—24no—
728#117—948no—
729#117—948no—
730#117—944no—
731#117—944no—
732#117—944no—
733C2×C4⋊C4—472no—
734C2×C4⋊C4—472no—
735C2×C4⋊C4—471no—
736C2×C4⋊C4—471no—
737C2×C4⋊C4—471no—
738C2×C4⋊C4—471no—
739C2×C4⋊C4—471no—
740C2×C4⋊C4—472no—
741C2×C4⋊C4—472no—
742C2×C4⋊C4—472no—
743C2×C4⋊C4—472no—
744C2×C4⋊C4—472no—
745C2×C4⋊C4—472no—
746C2×C4⋊C4—944no—
747C2×C4⋊C4—944no—
748C2×C4⋊C4—944no—
749C2×C4⋊C4—948no—
750C2×C4⋊C4—948no—
751C2×C4⋊C4C22×D4711yescharacteristic
752C2×C4⋊C4C22×D4711yescharacteristic
753C2×C4⋊C4C22×D4711yescharacteristic
754C2×C4⋊C4C22×D4712yes—
755C2×C4⋊C4C22×D4712yes—
756C2×C22⋊C4—472no—
757C2×C22⋊C4—471no—
758C2×C22⋊C4—471no—
759C2×C22⋊C4—472no—
760C2×C22⋊C4—472no—
761C2×C22⋊C4—472no—
762C2×C22⋊C4—472no—
763C2×C22⋊C4—472no—
764C2×C22⋊C4—471no—
765C2×C22⋊C4—471no—
766C2×C22⋊C4—471no—
767C2×C22⋊C4—471no—
768C2×C22⋊C4—472no—
769C2×C22⋊C4—472no—
770C2×C22⋊C4—472no—
771C2×C22⋊C4—472no—
772C2×C22⋊C4—472no—
773C2×C22⋊C4—472no—
774C2×C22⋊C4—944no—
775C2×C22⋊C4—948no—
776C2×C22⋊C4—948no—
777C2×C22⋊C4—948no—
778C2×C22⋊C4—944no—
779C2×C22⋊C4—948no—
780C2×C22⋊C4C22×D4712yes—
781C2×C22⋊C4C22×D4711yescharacteristic
782C2×C22⋊C4C22×D4711yescharacteristic
783C2×C22⋊C4C22×D4712yes—
784C2×C22⋊C4C22×D4712yes—
785C2×C22⋊C4C22×D4712yes—
786C2×C42—472no—
787C2×C42—472no—
788C2×C42—471no—
789C2×C42—471no—
790C2×C42—472no—
791C2×C42—472no—
792C2×C42—472no—
793C2×C42—471no—
794C2×C42—472no—
795C2×C42—948no—
796C2×C42—944no—
797C2×C42—948no—
798C2×C42C22×D4712yes—
799C2×C42C22×D4711yescharacteristic
800C2×C42C22×D4712yes—
801#95—472no—
802#95—472no—
803#95—472no—
804#95—472no—
805#95—471no—
806#95—472no—
807#95—472no—
808#95—472no—
809#95—471no—
810#95—472no—
811#95—472no—
812#95—472no—
813#95—472no—
814#95—472no—
815#95—472no—
816#95—472no—
817#95C22×D4712yes—
818#95C22×D4711yescharacteristic
819#95C22×D4712yes—
820#95C22×D4711yescharacteristic
821#95C22×D4712yes—
822#95C22×D4712yes—
823C24—471no—
824C24—474no—
825C24—474no—
826C24—471no—
827C24—471no—
828C24—942no—
829C24—944no—
830C24—944no—
831C24—944no—
832C24—944no—
833C24—942no—
834C24—942no—
835C24—942no—
836C24C23×D4711yescharacteristic
837C24C23×D4711yescharacteristic
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—22no—
841C2×D4—942no—
842C2×D4—942no—
843C2×D4—942no—
844C2×D4—942no—
845C2×D4—9432no—
846C2×D4—942no—
847C2×D4—942no—
848C2×D4—942no—
849C2×D4—942no—
850C2×D4—942no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—471no—
855C22×C4—474no—
856C22×C4—478no—
857C22×C4—474no—
858C22×C4—472no—
859C22×C4—471no—
860C22×C4—471no—
861C22×C4—474no—
862C22×C4—474no—
863C22×C4—474no—
864C22×C4—478no—
865C22×C4—474no—
866C22×C4—472no—
867C22×C4—471no—
868C22×C4—471no—
869C22×C4—472no—
870C22×C4—472no—
871C22×C4—944no—
872C22×C4—9432no—
873C22×C4—942no—
874C22×C4—944no—
875C22×C4—942no—
876C22×C4—944no—
877C22×C4—944no—
878C22×C4—944no—
879C22×C4—942no—
880C22×C4—942no—
881C22×C4—944no—
882C22×C4—944no—
883C22×C4—944no—
884C22×C4—942no—
885C22×C4—944no—
886C22×C4—944no—
887C22×C4—944no—
888C22×C4—944no—
889C22×C4—944no—
890C22×C4—944no—
891C22×C4—944no—
892C22×C4—944no—
893C22×C4—944no—
894C22×C4—942no—
895C22×C4—944no—
896C22×C4—944no—
897C22×C4—942no—
898C22×C4—944no—
899C22×C4—18816no—
900C22×C4D4×D4714yes—
901C22×C4C23×D4712yes—
902C22×C4C23×D4711yescharacteristic
903C22×C4C23×D4711yescharacteristic
904C22×C4C23×D4712yes—
905C22×C4C23×D4712yes—
906C22×C4C23×D4711yescharacteristic
907C22×C4C23×D4712yes—
908C22×C4C23×D4711yescharacteristic
909C22×C4C23×D4711yescharacteristic
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—944no—
916C4⋊C4—944no—
917C4⋊C4—944no—
918C4⋊C4—944no—
919C4⋊C4—944no—
920C4⋊C4—942no—
921C4⋊C4—944no—
922C4⋊C4—942no—
923C4⋊C4—942no—
924C4⋊C4—942no—
925C4⋊C4—942no—
926C4⋊C4—944no—
927C4⋊C4—944no—
928C22⋊C4—24no—
929C22⋊C4—22no—
930C22⋊C4—24no—
931C22⋊C4—22no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—944no—
935C22⋊C4—944no—
936C22⋊C4—942no—
937C22⋊C4—944no—
938C22⋊C4—944no—
939C22⋊C4—944no—
940C22⋊C4—944no—
941C22⋊C4—942no—
942C22⋊C4—942no—
943C22⋊C4—944no—
944C22⋊C4—944no—
945C22⋊C4—942no—
946C22⋊C4—944no—
947C22⋊C4—942no—
948C22⋊C4—944no—
949C22⋊C4—942no—
950C22⋊C4—944no—
951C22⋊C4—944no—
952C42—24no—
953C42—22no—
954C42—24no—
955C42—944no—
956C42—944no—
957C42—944no—
958C42—944no—
959C42—942no—
960C42—942no—
961C42—944no—
962C42—942no—
963C42—944no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—472no—
973C23—474no—
974C23—472no—
975C23—474no—
976C23—472no—
977C23—472no—
978C23—472no—
979C23—948no—
980C23—948no—
981C23—948no—
982C23—9416no—
983C23—948no—
984C23—941no—
985C23—942no—
986C23—942no—
987C23—942no—
988C23—942no—
989C23—941no—
990C23—941no—
991C23—941no—
992C23—1884no—
993C23—1888no—
994C23—1888no—
995C23—1888no—
996C23—1884no—
997C23C2×D4×D4712yes—
998C23#41×D4712yes—
999C23C24×D4711yescharacteristic
1000D4—28no—
1001D4—948no—
1002D4—948no—
1003D4—948no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—28no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—44no—
1024C2×C4—472no—
1025C2×C4—474no—
1026C2×C4—4716no—
1027C2×C4—472no—
1028C2×C4—474no—
1029C2×C4—472no—
1030C2×C4—948no—
1031C2×C4—9416no—
1032C2×C4—948no—
1033C2×C4—948no—
1034C2×C4—948no—
1035C2×C4—941no—
1036C2×C4—942no—
1037C2×C4—942no—
1038C2×C4—942no—
1039C2×C4—941no—
1040C2×C4—948no—
1041C2×C4—941no—
1042C2×C4—942no—
1043C2×C4—942no—
1044C2×C4—941no—
1045C2×C4—942no—
1046C2×C4—942no—
1047C2×C4—942no—
1048C2×C4—942no—
1049C2×C4—942no—
1050C2×C4—942no—
1051C2×C4—942no—
1052C2×C4—942no—
1053C2×C4—942no—
1054C2×C4—1884no—
1055C2×C4—1888no—
1056C2×C4—1888no—
1057C2×C4—1884no—
1058C2×C4—1888no—
1059C2×C4—1884no—
1060C2×C4—1884no—
1061C2×C4—1884no—
1062C2×C4C2×D4×D4712yes—
1063C2×C4C2×D4×D4712yes—
1064C2×C4#41×D4714yes—
1065C2×C4#41×D4712yes—
1066C2×C4#41×D4714yes—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—24no—
1071C22—22no—
1072C22—41no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—41no—
1077C22—474no—
1078C22—474no—
1079C22—478no—
1080C22—478no—
1081C22—474no—
1082C22—942no—
1083C22—942no—
1084C22—942no—
1085C22—944no—
1086C22—942no—
1087C22—18816no—
1088C22—18816no—
1089C22—1881no—
1090C22—1882no—
1091C22—1882no—
1092C22—1882no—
1093C22—1881no—
1094C22C22×D4×D4711yescharacteristic
1095C22C2×#41×D4712yes—
1096C22C2×#41×D4711yescharacteristic
1097C22C2×#41×D4711yescharacteristic
1098C22C2×#41×D4712yes—
1099C4—22no—
1100C4—22no—
1101C4—24no—
1102C4—41no—
1103C4—42no—
1104C4—42no—
1105C4—41no—
1106C4—42no—
1107C4—474no—
1108C4—942no—
1109C4—942no—
1110C4—944no—
1111C4—1881no—
1112C4—1882no—
1113C4—1882no—
1114C4—1881no—
1115C4—1882no—
1116C4#123×D4714yes—
1117C2—42no—
1118C2—42no—
1119C2—478no—
1120C2—1882no—
1121C2—1882no—
1122C2C2×#123×D4711yescharacteristic
1123C2#525×D4711yescharacteristic
1124C2#529×D4712yes—
1125C2#529×D4712yes—
1126C2#532×D4711yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2395C2
prime radicalC22×D4×D47C22
hypercenter#2395D47
hypocenterC47C2×#2395
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#117×D47C2semidirect
3. #20246654C2semidirect
4. #20246653C2semidirect
5. #20246652C2semidirect
6. #20246651C2semidirect
7. #20246650C2semidirect
8. #20246649C2semidirect
9. #20246648C2semidirect
10. #20246647C2semidirect
11. #20246646C2semidirect
12. #20246645C2semidirect
13. #20246644C2semidirect
14. #400×D47C2semidirect
15. #399×D47C2semidirect
16. #398×D47C2semidirect
17. #397×D47C2semidirect
18. #397×D47C2semidirect
20. C4×C4⋊C4×D47C2semidirect
21. C4×C22⋊C4×D47C2semidirect
22. C4×C22⋊C4×D47C2semidirect
23. C47×#2395C2semidirect
35. C2×#13093983C22semidirect
36. C2×#13093982C22semidirect
37. C2×#13093982C22semidirect
38. C2×#13093981C22semidirect
39. C2×#13093980C22semidirect
55. #15689065C22semidirect
56. #15689064C22semidirect
57. #15689063C22semidirect
58. #15689062C22semidirect
59. #15689061C22semidirect
60. #15689060C22semidirect
61. #15689059C22semidirect
62. #15689059C22semidirect
63. #15689058C22semidirect
64. #15689058C22semidirect
65. #15689057C22semidirect
66. #15689056C22semidirect
67. #15689055C22semidirect
68. #15689054C22semidirect
69. #15689053C22semidirect
70. #15689052C22semidirect
71. #15689052C22semidirect
72. #15689052C22semidirect
73. #15689051C22semidirect
74. #15689051C22semidirect
75. #15689051C22semidirect
76. #15689050C22semidirect
77. #15689050C22semidirect
78. #15689049C22semidirect
79. #15689049C22semidirect
80. #15689048C22semidirect
81. #15689048C22semidirect
89. C4⋊C4×Dic47C22semidirect
90. C4⋊C4×Dic47C22semidirect
91. C4×Dic47⋊C4C22semidirect
92. C4×Dic47⋊C4C22semidirect
93. C4×C4⋊Dic47C22semidirect
94. #15688974C22semidirect
95. #15688974C22semidirect
96. C22⋊C4×Dic47C22semidirect
97. C22⋊C4×Dic47C22semidirect
98. C22⋊C4×Dic47C22semidirect
99. C4×(C2×D47)⋊C4C22semidirect
100. C4×(C2×D47)⋊C4C22semidirect
101. C4×(C2×D47)⋊C4C22semidirect
102. C4×C22⋊Dic47C22semidirect
103. C4×C22⋊Dic47C22semidirect
104. #15688970C22semidirect
105. #15688970C22semidirect
106. #15688970C22semidirect
107. #15688970C22semidirect
115. C2×#117×C47C22semidirect
116. C47×#400C22semidirect
117. C47×#399C22semidirect
118. C47×#398C22semidirect
119. C47×#397C22semidirect
120. C47×#397C22semidirect
122. C4×C4⋊C4×C47C22semidirect
123. C4×C22⋊C4×C47C22semidirect
124. C4×C22⋊C4×C47C22semidirect
567. #2395D47direct (N × H)
586. D47#2395direct (N × H)
605. C2×#117C2×D47semidirect
625. #400C2×D47semidirect
631. #399C2×D47semidirect
637. #398C2×D47semidirect
650. #397C2×D47semidirect
651. #397C2×D47semidirect
667. C4×C4⋊C4C2×D47semidirect
680. C4×C22⋊C4C2×D47semidirect
681. C4×C22⋊C4C2×D47semidirect
688. C47C2×#2395semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D4×D472
C2×#117×D472
#202466542
#202466532
#202466522
#202466512
#202466502
#202466492
#202466482
#202466472
#202466462
#202466452
#202466442
#400×D472
#399×D472
#398×D472
#397×D472
#394×D472
C4×C4⋊C4×D472
C4×C22⋊C4×D472
C47×#23952
C2×#239547